Will I be eligible for government jobs after completing AMIE? I have a Polytechnic Diploma in civil engineering.

In many cases, you may. But, not in all govt. jobs. For example, in few public sector undertaking, it is not considered. As a matter of fact, AMIE is continuing education meant for working aspirants and hence suitable for promotions, higher education such as M.Tech, high-level UPSC exams, etc.